Global sensitivity analysis for optimization of the Trotter-Suzuki decomposition

The Trotter-Suzuki decomposition is one of the main approaches for realization of quantum simulations on digital quantum computers. Variance-based global sensitivity analysis (the Sobol method) is a wide used method which allows to decompose output variance of mathematical model into fractions allocated to different sources of uncertainty in inputs or sets of inputs of the model. Here we developed a method for application of the global sensitivity analysis to the optimization of Trotter-Suzuki decomposition. We show with a proof-of-concept example that this approach allows to reduce the number of exponentiations in the decomposition and provides a quantitative method for finding and truncation 'unimportant' terms in the system Hamiltonian.